The Electromagnetic Properties of Materials • Electrical conduction – – – –
Metals Semiconductors Insulators (dielectrics) Superconductors
• Magnetic materials
– Ferromagnetic materials – Others
• Photonic Materials (optical) – Transmission of light – Photoactive materials
• Photodetectors and photoconductors • Light emitters: LED, lasers
MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
The Electromagnetic Properties of Materials • Electrical conduction – – – –
Metals Semiconductors Insulators (dielectrics) Superconductors
• Magnetic materials
– Ferromagnetic materials – Others
• Photonic Materials (optical) – Transmission of light – Photoactive materials
• Photodetectors and photoconductors • Light emitters: LED, lasers
MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
Insulators (Dielectrics)
• Characteristics: conduction band E
EF
• Engineering uses
EG valence band
x
MSE 200A Fall, 2008
– Large band gap (> 2 eV) – Very low conductivity
– Separate conductors • No leakage current • No interference
– Support electric fields
• Store energy (capacitors) • Induce charge (MOSFET)
J.W. Morris, Jr. University of California, Berkeley
Insulators: Material Properties • Ability to insulate ⇒ critical field (Ec)
– Insulator separates conductors until E reaches Ec
• Support internal field ⇒ dielectric constant (ε)
– High ε ⇒ high induced charge for given voltage
• Capacitors: high ε ⇒ efficient energy storage • Oxide in MOSFET: high ε ⇒ low switching voltage
– Low ε ⇒ small induced charges
• “low-k” insulators essential for microelectronic packaging
• Energy dissipation from current ⇒ loss tangent (δ)
– Low δ ⇒ low rate of energy loss from propagating e-m fields
MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
Insulators: Breakdown Voltage • Insulator protects until
– E reaches Ec “breakdown” – Catastrophic increase in j at Ec – Example: lightning
j
E
e
e {e
• Common “cascade mechanism”
– Electron accelerated in field – Excites new carriers by collision – These accelerate in chain reaction
• Material and microstructure variables
E
– Band gap: Ec increases with EG – Purity: Ec usually increases with purity – Temperature: minimum at intermediate T
x MSE 200A Fall, 2008
Ec
• Few carriers at low T • Low mobility at high T
J.W. Morris, Jr. University of California, Berkeley
Dielectrics -Q - - - - - - - - - - - - - -
V
dielectric
d
+ + + + + + + + + + + + + +
+Q
Q = CV
C = capacitance
σ A = C(Ed)
D = electric displacement
σ = D = εε 0 E
ε ≥ 1 (= 1 in free space)
• Dielectrics (insulators) support internal fields
– The “dielectric constant” relates field to charge – Sometimes use “susceptibility” χ = ε - 1 (χ = 0 in free space)
MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
Source of the Dielectric Constant - Q
- - - - - - - - - - - - - -
+ + + + V d - - - - + + + + + + + + + + + + + +
+ Q
• Internal polarization – Dipoles align in applied field – Create reverse field (EI)
ε 0 E = ε 0 E0 − ε 0 E I = σ − P + + + + + + + +
P = ∑ pi = χ E
- - - - - - - - P
+ + + + + + + + - - - - - - - - + + + + + + + + - - - - - - - -
MSE 200A Fall, 2008
i
p i
D = σ = ε 0 E + P = εε 0 E P ε = 1+ ε0E
J.W. Morris, Jr. University of California, Berkeley
Polarization Mechanisms - Q
- - - - - - - - - - - - - -
+ + + + V d - - - - + + + + + + + + + + + + + +
+ Q
P
- - - - - - - - + + + + + + + +
p i
- - - - - - - - - - - - - -
V + - + - + d
+ + + + + + + + + + + + + +
+ Q
- MSE 200A Fall, 2008
– Large polar organics have big ε – Relatively slow response (like diffusion)
- - - - - - - - - Q
– Porous materials (large pores) – Slow response in insulators
• Molecular dipoles
+ + + + + + + + - - - - - - - - + + + + + + + +
• Space charges
• Ionic displacements
– Ionic crystals have moderate ε – Fast response (like optical phonon)
• Atomic dipole
– Small ε – Very fast response (plasmon frequency)
+
J.W. Morris, Jr. University of California, Berkeley
Influence of the Dielectric Constant - Q
- - - - - - - - - - - - - -
V
dielectric + + + + + + + + + + + + + +
d
1 1 U = DE = εε 0 E 2 2 2
+ Q
• For given σ (Q) increasing ε decreases field (E) • For given voltage drop (E), increasing ε increases Q (σ)
– Energy stored in a capacitor increases with ε – Induced charge between adjacent conductors increases with ε • MOSFET oxides need maximum ε • Insulators in microelectronic packaging need minimum ε • Both are major objectives in modern microelectronics – (many jobs, much money)
MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
Ultra-low Dielectric Constant - Q
- - - - - - - - - - - - - -
V
dielectric
• For a given voltage drop (E),
d
+ + + + + + + + + + + + + +
increasing ε increases Q (σ) ⇒ Induced charge increases with ε
+ Q
•
“Low-k” materials – Critical for applications in electronic packaging
•
Materials design – Organics based on non-polar molecules – Dense array of nanopores (ε = 1)
•
Materials issues – Mechanical integrity - must support device
MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
High Dielectric Constant - Ferroelectricity • Ferroelectric materials – BaTiO3 (for example) – Effective CsCl
+
• At high T (T > Tc)
– Central ion centered – No dipole moment
α
P
α ’
• At low T (T < Tc)
– Central ion displaces to create dipole – All neighboring cells displace parallel ⇒ Large net dipole moment
T MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
The Electromagnetic Properties of Materials •
Electrical conduction
•
Magnetic materials
•
Photonic Materials (optical)
– – – –
Metals Semiconductors Insulators (dielectrics) Superconductors
– Ferromagnetic materials – Others – Transmission of light – Photoactive materials
• Photodetectors and photoconductors • Light emitters: LED, lasers
MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
The Optical Properties of Materials: Photonic Materials • Beauty: one-half of the earliest materials science
– Pottery glazes(the origin of metals), paints and cosmetics – Jewelry - the development of metals and metalworking
• Information
– Window glass – Optical fibers (rapidly replacing copper wire)
• Light
– The electric light – LEDs and Lasers – Photodetectors and photoconductors
• Power
– Photovoltaics (solar cells) – Laser power transmission (welding, surface treatments)
MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
The Optical Properties of Materials: Photonic Materials •
“Optical” means the whole electromagnetic spectrum – From radio waves to γ-rays – Can be regarded as
• Waves in space • Particles with quantized energies
•
Light as waves
•
Light as particles
MSE 200A Fall, 2008
– Refraction and reflection at an interface (windows, light pipes, solarium) – Absorption and scattering (optical fibers) – Diffraction (x-ray and electron crystallography) – Transmission and absorption – Photodetectors and photoconductors: switches, photocopiers – Photoemitters: LEDs and lasers
J.W. Morris, Jr. University of California, Berkeley
Electromagnetic Waves in Free Space ¬ E H
• Wave carries electric and magnetic fields
– Oriented perpendicular to the direction of propagation – Wave: 2π k=
E = E 0 exp[−i( kx − ωt )]
– Particle: € MSE 200A Fall, 2008
ε = hν = ω
€ €
λ ω = 2πν ω = νλ = c k
(λ = wavelength) (ν = frequency) c = speed
J.W. Morris, Jr.
€
University of California, Berkeley
The Electromagnetic Spectrum
infrared
microwave
20
6
18
4
16
2
14 12 10 8
radio
6 4
MSE 200A Fall, 2008
0 -2 -4
-14 0.4 µm
-12 -10
log[wavelength(m)]
ultraviolet visible
log[frequency(Hz)]
x-ray
8
log[energy(eV)]
©- ray
22
1Å 1 nm
-8 -6
violet blue
0.5 µm green
1 µm
yellow 0.6 µm
-4
orange
1 mm -2
-6
0
-8
2
-10
4
red 1m
1 km
0.7 µm
• Visible light:
– λ ~ 0.4-1 µm – E ~ 1.2-3 eV
J.W. Morris, Jr. University of California, Berkeley
Light as a Wave • Propagation through free space at velocity, c • When light enter a material, it is – Refracted – Reflected – Attenuated incident transmitted reflected
MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
Refraction and Reflection at an Interface: Normal Incidence • Refraction:
– Wave “drags” charges – Friction slows propagation
incident transmitted
• Index of refraction (n)
reflected
– Property governing refraction – Related to dielectric constant: n= ε
Inside material:
E = E 0 exp[−i(kx − ωt)]
– Depends on frequency (dispersion) € n = n(ω ) = ε(ω )
λ0 k = nko ⇒ λ = n ω c v=
€
k
=
n
J.W. Morris, Jr.
MSE 200A Fall, 2008
University of California, Berkeley
€
€
€
Refraction at an Interface • Snells’ Law
Φ2
n1 sin φ1 = n 2 sin φ 2 – Light bends toward low-n region
n2
d
n1 Φ1
€
• The critical angle
– Light cannot exist region 1 if n1 φ2 > φc = sin n −1
2
– Principle of “light pipe” Optical fiber confines light by reflection MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
Reflection at an Interface • Normal incidence from n1 to n2 – Δn ⇒ reflection – Intensity thrown back
• Reflected intensity incident
n1
Ir (n 2 − n1 ) 2 R= = Ii (n 2 + n1 ) 2
n2 transmitted
reflected
• Transmitted intensity It 4n 2 T = = 1− R = € Ii (n1 + n 2 ) 2 • Note: depends on Δn – Not transparency
€ MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
Propagation of Light: Attenuation • IT is gradually attenuated
incident
• Mechanisms of attenuation
I
– Absorption – Rayleigh scattering
reflected
transmitted x
IT = I0 exp[−ηx ] MSE 200A Fall, 2008
• Mechanisms of absorption – Conduction electrons – Phonons – Electronic transitions • Valence • Core
J.W. Morris, Jr. University of California, Berkeley
Absorption: Insulator or Semiconductor conduction band
E
Ionic transitions valence band
x
E
Optical phonons
• Absorption by
MSE 200A Fall, 2008
– – – –
Optical phonons (solar panels) Ionic transitions (color) Band transitions (photoconductivity) Core transitions (x-ray spectroscopy)
J.W. Morris, Jr. University of California, Berkeley
Attenuation: Rayleigh Scattering
• Light scatters from heterogeneities
– Density fluctuations – Chemical heterogeneities – Defects and second-phase particles
• Only recently is it possible to produce clear, uniform glass – “As through a glass - darkly”
MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
Diffraction
œ
œ
d
•
Waves reflected from successive planes – Destructive interference unless
nλ = 2d sin θ
(Bragg’s Law)
– Bragg’s Law ⇒ strong intensity peak
•
Pattern of diffraction peaks identifies crystal structure – Use x-rays or electrons with λ of a few Å
€
MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
Electron Diffraction of “Intercritically Tempered Steel” • Electron microscopy – Photograph – Diffraction pattern
• Diffraction pattern
– Peaks from crystal planes – Pattern identifies phases – Ex.: bcc and fcc Fe present
• Combined analysis
– “Bright field” microstructure – Diffraction pattern shows phases – “Dark field” locates phases • Image diffraction spot
MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
Exploiting the Light as a Wave: Examples • Optical fibers – Transparent pipes that transmit light – Note that “light” need not be visible • GaAs systems operate in the infrared
• Greenhouses and solar heaters – Glass containers that let light in, – Then trap its energy for heat
MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
Optical Fibers
•
Require
•
Gradient fibers
– – – –
Small diameter to minimize surface loss Perfect cylinder to minimize surface scattering Exceptional purity to suppress absorption Exceptional uniformity to suppress Rayleigh scattering
– Rays that reflect from surface travel farther than rays on-axis • Loss of coherence and information
– Want gradient in n such that n lower on outside • Rays that reflect from surface move faster
– Can adjust n with solute additions
MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
Absorption: The “Greenhouse” Effect conduction band
E
Ionic transitions valence band
x
E
Optical phonons
• Absorption by
MSE 200A Fall, 2008
– – – –
Optical phonons (solar panels) Ionic transitions (color) Band transitions (photoconductivity) Core transitions (x-ray spectroscopy)
J.W. Morris, Jr. University of California, Berkeley
The Solarium and Solar Heater
glass
earth
MSE 200A Fall, 2008
•
Mechanism is glass
•
Sunlight enters
– transparent in the visible – Opaque in the infrared – Rays are absorbed and re-emitted in the infrared – Re-emitted rays cannot penetrate glass – Solar energy is trapped inside
J.W. Morris, Jr. University of California, Berkeley
Light as a Particle: Photons • Transparency and color • Photodetectors
– Photoconductors – Photoelectronics – Photocopiers
• Photoemitters
– Phosphors – Light-emitting diodes (LED) – Lasers
MSE 200A Fall, 2008
J.W. Morris, Jr. University of California, Berkeley
